5x^2+53x=22

Solution for 5x^2+53x=22 equation:

5x^2+53x=22

We move all terms to the left:

5x^2+53x-(22)=0

a = 5; b = 53; c = -22;
Δ = b2-4ac
Δ = 532-4·5·(-22)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-57}{2*5}=\frac{-110}{10}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+57}{2*5}=\frac{4}{10}
=2/5
$